The need for an improved telecommunications network with a much higher capacity, simpler control, lower capital cost and lower operating cost is well recognized. For the past two decades, researches have been rethinking the art of telecommunication networking to overcome the difficulties arising from the rapid untidy growth of the Internet.
Using switches of m×m dimension each, m>1, to construct a three-stage network, the dimension of the network would be m2×m2. With m=64, for example, a network of 4096 input ports and 4096 output port can be realized, with each connection traversing three switches.
Using switches of m×m dimension each to construct a five-stage network, the dimension of the network would be m3×m3. With m=64, a network of 262144 input ports and 262144 output port can be realized. With each connection traversing three intermediate switches, a significant dilation (inner expansion) would be needed where the inner capacity of the network substantially exceeds its access capacity.
The dimension of a multi-stage network grows rapidly as the number of stages increases. However, the complexity increases, and the performance deteriorates, as the number of stages increases. There is a need to explore switching methods which enable constructing large-scale networks while reducing the number of switching stages traversed.